Exponential extension distribution: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the exponential extension distribution

Description

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the exponential extension distribution.

Usage

se_nh(alpha, beta)
re_nh(alpha, beta, delta)
hce_nh(alpha, beta, delta)
ae_nh(alpha, beta, delta)

Value

The functions se_nh, re_nh, hce_nh, and ae_nh provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the exponential extension distribution and $\delta$.

Arguments

alpha: The strictly positive parameter of the exponential extension distribution ($\alpha > 0$).
beta: The strictly positive parameter of the exponential extension distribution ($\beta > 0$).
delta: The strictly positive parameter ($\delta > 0$) and ($\delta \ne 1$).

Author

Muhammad Imran, Christophe Chesneau and Farrukh Jamal

R implementation and documentation: Muhammad Imran <imranshakoor84@yahoo.com>, Christophe Chesneau <christophe.chesneau@unicaen.fr> and Farrukh Jamal farrukh.jamal@iub.edu.pk.

Details

The following is the probability density function of the exponential extension distribution: $$ f(x)=\alpha\beta(1+\alpha x)^{\beta-1}e^{1-(1+\alpha x)^{\beta}}, $$ where $x > 0$, $\alpha > 0$ and $\beta > 0$.

References

Nadarajah, S., & Haghighi, F. (2011). An extension of the exponential distribution. Statistics, 45(6), 543-558.

Examples

Run this code

se_nh(1.2, 0.2)
delta <- c(1.5, 2, 3)
re_nh(1.2, 0.2, delta)
hce_nh(1.2, 0.2, delta)
ae_nh(1.2, 0.2, delta)

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